Calculate Q1, D7 and P58 from the following data and interpret the results.

Weight 0-10 10-15 20-25 25-30 30-35 35-40 40-45 45-50 50-60
No, of person 4 8 30 15 13 6 4 4 1

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Solution:

Since the classes are unequal so adjustment is to be made before calculating.

Weight No. of Person (f) c.f.
0-5 2 2
5-10 2 4
10-15 8 12
15-20 15 27
20-25 15 42
25-30 15 57
30-35 13 70
35-40 6 76
40-45 4 80
45-50 4 84
50-55 0.5 84.5
55-60 0.5 85
N = 85

Now,

For Q1:

Q1 = \(\left ( \frac{N}{4} \right )^{th} \enspace item\)

= \(\left ( \frac{85}{4} \right )^{th} \enspace item\) = 21.25th item

In c.f column, the value just greater than 25.25 is 27. so, class is 15 – 20

Then,

Q1 = \(L + \frac{\frac{N}{4} – c.f.}{f} \times h\)

= \(15 + \frac{21.25 – 12}{15} \times 5\)

= 18.08

For D7:

D7 = \(\left ( 7 \times \frac{N}{10} \right )^{th} \enspace item\)

= \(\left ( 7 \times \frac{85}{10} \right )^{th} \enspace item\) = 59.5th item

In c.f column, the value just greater than 59.5 is 70. so, class is 30-35

Then,

D7 = \(L + \frac{\frac{7N}{10} – c.f.}{f} \times h\)

= \(30 + \frac{59.5 – 57}{13} \times 5\)

= 30.96

For P58:

P58 = \(\left (\frac{58 N}{100} \right )^{th} \enspace item\)

= \(\left ( 7 \times \frac{58 \times 85}{100} \right )^{th} \enspace item\) = 49.3th item

In c.f column, the value just greater than 49.3 is 57. so, class is 25-30

Then,

P58 = \(L + \frac{\frac{58N}{100} – c.f.}{f} \times h\)

= \(25 + \frac{49.3 – 43}{15} \times 5\)

= 26.43

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